Some recurrence relations associated with the Alavi sequence

K. T. Atanassov and A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 12, 2006, Number 3, Pages 20–24
Full paper (PDF, 42 Kb)


Authors and affiliations

K. T. Atanassov
CBME – Bulgarian Academy of Sciences
Acad. G. Bonchev Str. Block 105, Sofia 1113, Bulgaria

A. G. Shannon
Warrane College, University of New South Wales, NSW 1465, Australia &
KvB Institute of Technology, North Sydney, NSW 2060, Australia


This paper considers a modification of the Fibonacci sequence which results in the third order Alavi sequence. Not only are the initial terms quite general but the rule of formation is also modified. Some results are proved to illustrate the underlying structure of the sequence and its relation to known results in the literature. The paper concludes with a suggestion for further research with an arbitrary order extension.

AMS Classification

  • 11B39
  • 11B65


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Cite this paper

Atanassov, K. T., and Shannon, A. G. (2006). Some recurrence relations associated with the Alavi sequence. Notes on Number Theory and Discrete Mathematics, 12(3), 20-24.

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